Liquid Coating with Variable Thermal Conductivity on a Pipe under Influence of Thermal Radiation and Heat Generation
DOI:
https://doi.org/10.37934/cfdl.14.11.102118Keywords:
Carreau Fluid, thermal radiation, variable thermal conductivity, heat generationAbstract
Flow over a pipe or an elongated cylinder is widely applied in many engineering processes like wire coating and pipe coating. This encourages the present study to examine the fluid flow and heat transfer over a horizontal stretching cylinder with the impact of temperature-reliant thermal conductivity and thermal radiation. The influence of heat generation is also considered. The Carreau rheology model is applied to represent the liquid coating. The similarity technique is used to simplify the developed governing equations and then solved by the homotopy analysis method. The effects of the pertinent parameters such as the thermal conductivity parameter and Weissenberg number on the fluid field and heat transfer are studied by applying the calculated series of analytical solutions, which are scrutinized through graphs and tables. The Nusselt number has a negative function with the radiation and thermal conductivity parameters. Furthermore, the Weissenberg number affects the velocity and temperature profiles differently in conditions n < 1 and n ≥ 1, respectively. The present results are essential in optimizing the pipe coating process.Downloads
References
Carreau, Pierre J. "Rheological equations from molecular network theories." Transactions of the Society of Rheology 16, no. 1 (1972): 99-127. https://doi.org/10.1122/1.549276
El Misery, A. E. M., and M. F. Abd El Kareem. "Separation in the flow through peristaltic motion of a Carreau fluid in uniform tube." Physica A: Statistical Mechanics and Its Applications 343 (2004): 1-14. https://doi.org/10.1016/j.physa.2004.05.072
Akbar, Noreen Sher, and S. Nadeem. "Combined effects of heat and chemical reactions on the peristaltic flow of Carreau fluid model in a diverging tube." International journal for numerical methods in fluids 67, no. 12 (2011): 1818-1832. https://doi.org/10.1002/fld.2447
Akbar, N. S., S. Nadeem, Rizwan Ul Haq, and Shiwei Ye. "MHD stagnation point flow of Carreau fluid toward a permeable shrinking sheet: Dual solutions." Ain Shams Engineering Journal 5, no. 4 (2014): 1233-1239. https://doi.org/10.1016/j.asej.2014.05.006
Hayat, Tasawar, Sadia Asad, Meraj Mustafa, and Ahmed Alsaedi. "Boundary layer flow of Carreau fluid over a convectively heated stretching sheet." Applied Mathematics and Computation 246 (2014): 12-22. https://doi.org/10.1016/j.amc.2014.07.083
Khan, Masood. "Boundary layer flow and heat transfer to Carreau fluid over a nonlinear stretching sheet." AIP Advances 5, no. 10 (2015): 107203. https://doi.org/10.1063/1.4932627
Hayat, T., M. Waqas, S. A. Shehzad, and A. Alsaedi. "Stretched flow of Carreau nanofluid with convective boundary condition." Pramana 86, no. 1 (2016): 3-17. https://doi.org/10.1007/s12043-015-1137-y
Khan, M., M. Irfan, W. A. Khan, and A. S. Alshomrani. "A new modeling for 3D Carreau fluid flow considering nonlinear thermal radiation." Results in physics 7 (2017): 2692-2704. https://doi.org/10.1016/j.rinp.2017.07.024
Wang, Ch Y. "Fluid flow due to a stretching cylinder." The Physics of fluids 31, no. 3 (1988): 466-468. https://doi.org/10.1063/1.866827
Salahuddin, T. "Carreau fluid model towards a stretching cylinder: Using Keller box and shooting method." Ain Shams Engineering Journal 11, no. 2 (2020): 495-500. https://doi.org/10.1016/j.asej.2017.03.016
Khan, Masood, and Ali Saleh Alshomrani. "Characteristics of melting heat transfer during flow of Carreau fluid induced by a stretching cylinder." The European Physical Journal E 40, no. 1 (2017): 1-9. https://doi.org/10.1140/epje/i2017-11495-6
Salahuddin, T., Arif Hussain, M. Y. Malik, M. Awais, and Mair Khan. "Carreau nanofluid impinging over a stretching cylinder with generalized slip effects: using finite difference scheme." Results in physics 7 (2017): 3090-3099. https://doi.org/10.1016/j.rinp.2017.07.036
Hayat, T., Ikram Ullah, B. Ahmad, and A. Alsaedi. "Radiative flow of Carreau liquid in presence of Newtonian heating and chemical reaction." Results in Physics 7 (2017): 715-722. https://doi.org/10.1016/j.rinp.2017.01.019
Khan, Imad, M. Y. Malik, Arif Hussain, and Mair Khan. "Magnetohydrodynamics Carreau nanofluid flow over an inclined convective heated stretching cylinder with Joule heating." Results in physics 7 (2017): 4001-4012. https://doi.org/10.1016/j.rinp.2017.10.015
Gangadhar, K., K. V. Ramana, Oluwole Daniel Makinde, and B. Rushi Kumar. "MHD flow of a Carreau fluid past a stretching cylinder with Cattaneo-Christov heat flux using spectral relaxation method." In Defect and Diffusion Forum, vol. 387, pp. 91-105. Trans Tech Publications Ltd, 2018. https://doi.org/10.4028/www.scientific.net/DDF.387.91
Gopal, D., and N. Kishan. "Unsteady flow of a Carreau fluid over a shrinking cylinder in the occurrence of various parameter effects." In AIP Conference proceedings, vol. 2104, no. 1, p. 020004. AIP Publishing LLC, 2019. https://doi.org/10.1063/1.5100372
Song, Ying-Qing, Hassan Waqas, Kamel Al-Khaled, Umar Farooq, Soumaya Gouadria, Muhammad Imran, Sami Ullah Khan, M. Ijaz Khan, Sumaira Qayyum, and Qiu-Hong Shi. "Aspects of thermal diffusivity and melting phenomenon in Carreau nanofluid flow confined by nonlinear stretching cylinder with convective Marangoni boundary constraints." Mathematics and Computers in Simulation 195 (2022): 138-150. https://doi.org/10.1016/j.matcom.2022.01.001
Akram, Mohammad, Wasim Jamshed, B. Shankar Goud, Amjad Ali Pasha, Tanveer Sajid, M. M. Rahman, Misbah Arshad, and Wajaree Weera. "Irregular heat source impact on carreau nanofluid flowing via exponential expanding cylinder: A thermal case study." Case Studies in Thermal Engineering (2022): 102171. https://doi.org/10.1016/j.csite.2022.102171
Kardri, Mahani Ahmad, Norfifah Bachok, Norihan Md Arifin, Fadzilah Md Ali, and Yong Faezah Rahim. "Magnetohydrodynamic Flow Past a Nonlinear Stretching or Shrinking Cylinder in Nanofluid with Viscous Dissipation and Heat Generation Effect." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 90, no. 1 (2022): 102-114. https://doi.org/10.37934/arfmts.90.1.102114
Chiam, TC0914. "Heat transfer in a fluid with variable thermal conductivity over a linearly stretching sheet." Acta mechanica 129, no. 1 (1998): 63-72. https://doi.org/10.1007/BF01379650
Arunachalam, M., and N. R. Rajappa. "Thermal boundary layer in liquid metals with variable thermal conductivity." Flow, Turbulence and Combustion 34, no. 2 (1978): 179-187. https://doi.org/10.1007/BF00418866
Kays, W.M., Convective heat and mass transfer. 2011: Tata McGraw-Hill Education.
Arunachalam, M., and N. R. Rajappa. "Forced convection in liquid metals with variable thermal conductivity and capacity." Acta Mechanica 31, no. 1 (1978): 25-31. https://doi.org/10.1007/BF01261185
Khan, Ambreen A., S. Naeem, R. Ellahi, Sadiq M. Sait, and K. Vafai. "Dufour and Soret effects on Darcy-Forchheimer flow of second-grade fluid with the variable magnetic field and thermal conductivity." International Journal of Numerical Methods for Heat & Fluid Flow (2020). https://doi.org/10.1108/HFF-11-2019-0837
Swain, Kharabela, Basavarajappa Mahanthesh, and Fateh Mebarek‐Oudina. "Heat transport and stagnation‐point flow of magnetized nanoliquid with variable thermal conductivity, Brownian moment, and thermophoresis aspects." Heat Transfer 50, no. 1 (2021): 754-767. https://doi.org/10.1002/htj.21902
Khan, Sami Ullah, and Sabir Ali Shehzad. "Electrical MHD Carreau nanofluid over porous oscillatory stretching surface with variable thermal conductivity: applications of thermal extrusion system." Physica A: Statistical Mechanics and its Applications 550 (2020): 124132. https://doi.org/10.1016/j.physa.2020.124132
Abbas, Tariq, Sajid Rehman, Rehan Ali Shah, Muhammad Idrees, and Mubashir Qayyum. "Analysis of MHD Carreau fluid flow over a stretching permeable sheet with variable viscosity and thermal conductivity." Physica A: Statistical Mechanics and its Applications 551 (2020): 124225. https://doi.org/10.1016/j.physa.2020.124225
Yin, Junfeng, Xianqin Zhang, M. Israr Ur Rehman, and Aamir Hamid. "Thermal radiation aspect of bioconvection flow of magnetized Sisko nanofluid along a stretching cylinder with swimming microorganisms." Case Studies in Thermal Engineering 30 (2022): 101771. https://doi.org/10.1016/j.csite.2022.101771
Nabwey, Hossam A., Sumayyah I. Alshber, Ahmed M. Rashad, and Abd El Nasser Mahdy. "Influence of bioconvection and chemical reaction on magneto—Carreau nanofluid flow through an inclined cylinder." Mathematics 10, no. 3 (2022): 504. https://doi.org/10.3390/math10030504
Hayat, T., S. Asad, and A. Alsaedi. "Flow of variable thermal conductivity fluid due to inclined stretching cylinder with viscous dissipation and thermal radiation." Applied Mathematics and Mechanics 35, no. 6 (2014): 717-728. https://doi.org/10.1007/s10483-014-1824-6
Jain, Shalini, and Amit Parmar. "Radiation effect on MHD williamson fluid flow over stretching cylinder through porous medium with heat source." In Applications of Fluid Dynamics, pp. 61-78. Springer, Singapore, 2018. https://doi.org/10.1007/978-981-10-5329-0_5
Salahuddin, T., M. Y Malik, Arif Hussain, and S. Bilal. "Combined effects of variable thermal conductivity and MHD flow on pseudoplastic fluid over a stretching cylinder by using Keller box method." Information Sciences Letters 5, no. 1 (2016): 2. https://doi.org/10.18576/isl/050102
Malik, M. Y., M. Bibi, Farzana Khan, and T. Salahuddin. "Numerical solution of Williamson fluid flow past a stretching cylinder and heat transfer with variable thermal conductivity and heat generation/absorption." AIP Advances 6, no. 3 (2016): 035101. https://doi.org/10.1063/1.4943398
Rangi, Rekha R., and Naseem Ahmad. "Boundary layer flow past a stretching cylinder and heat transfer with variable thermal conductivity." (2012). https://doi.org/10.4236/am.2012.33032
Ewis, Karem Mahmoud. "Effects of Variable Thermal Conductivity and Grashof Number on Non-Darcian Natural Convection Flow of Viscoelastic Fluids with Non Linear Radiation and Dissipations." Journal of Advanced Research in Applied Sciences and Engineering Technology 22, no. 1 (2021): 69-80. https://doi.org/10.37934/araset.22.1.6980
Liao, Shijun. Beyond perturbation: introduction to the homotopy analysis method. Chapman and Hall/CRC, 2003.
Liao, Shijun. "Notes on the homotopy analysis method: some definitions and theorems." Communications in Nonlinear Science and Numerical Simulation 14, no. 4 (2009): 983-997. https://doi.org/10.1016/j.cnsns.2008.04.013
Liao, Shijun. Homotopy analysis method in nonlinear differential equations. Beijing: Higher education press, 2012. https://doi.org/10.1007/978-3-642-25132-0
Patel, Vijay K., and Jigisha U. Pandya. "The Consequences of Thermal Radiation and Chemical Reactions on Magneto-hydrodynamics in Two Dimensions over a Stretching Sheet with Jeffrey Fluid." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 95, no. 1 (2022): 121-144. https://doi.org/10.37934/arfmts.95.1.121144
Thirupathi, Gurrala, Kamatam Govardhan, and Ganji Narender. "Radiative Magnetohydrodynamics Casson Nanofluid Flow and Heat and Mass Transfer past on Nonlinear Stretching Surface." Journal of Advanced Research in Numerical Heat Transfer 6, no. 1 (2021): 1-21. https://doi.org/10.3762/bxiv.2021.65.v1
Hayat, T., M. S. Anwar, M. Farooq, and A. Alsaedi. "MHD stagnation point flow of second grade fluid over a stretching cylinder with heat and mass transfer." International Journal of Nonlinear Sciences and Numerical Simulation 15, no. 6 (2014): 365-376. https://doi.org/10.1515/ijnsns-2013-0104
Elbashbeshy, E. M. A., T. G. Emam, M. S. El-Azab, and K. M. Abdelgaber. "Effect of magnetic field on flow and heat transfer over a stretching horizontal cylinder in the presence of a heat source/sink with suction/injection." J. Appl. Mech. Eng 1, no. 1 (2012): 1-5. https://doi.org/10.4172/2168-9873.1000106
Poply, Vikas, Phool Singh, and K. K. Chaudhary. "Analysis of laminar boundary layer flow along a stretching cylinder in the presence of thermal radiation." WSEAS Trans Fluid Mech 8, no. 4 (2013): 159-164.